Well that would be very similar to Nuvo Auz, the illegally joined Trill. (Nuvo is a sleezeball ex drug-dealer and Auz, the symbiont, is a colossal snob, resulting in one confused entity.) I'm thinking I'll make Charleston the doctor. Since Starfleet saved her life, she wants to return the favor, while also partaking in exploration. On her own planet she's regarded as something of a veterinarian for those cute little Humanoids.
Having two faces from the same body looking at you with a diagnostician's eye, though...or being able to do two things at once. What if your non-humanoid can project herself somewhere, which would allow her to stay where she is in case needed on the ship, and at the same time, go on missions? Multitasker. Did you see my earlier suggestion about a Scalosian?